Math
Triangular Prism Calculator
The triangular prism calculator finds the volume and surface area of a prism with triangular ends.
Enter the three sides of the triangle and the prism length for a complete answer (volume, lateral area, total area), or just the triangle's base and height when you only need the volume.
Each side must be shorter than the other two combined.
How far the triangle is extruded — the distance between the two triangular ends.
Pick the unit your measurements use. Area is reported in square units and volume in cubic units.
Try an example
Result
Volume
—
- Volume with units
- —
- Triangle (end) area
- —
- Lateral area (three rectangles)
- —
- Total surface area
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- Capacity
- —
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Study path
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What the triangular prism calculator solves
The triangular prism calculator finds the volume and surface area of a prism with triangular ends. Enter the three sides of the triangle and the prism length for a complete answer (volume, lateral area, total area), or just the triangle's base and height when you only need the volume.
Formula
How to use it
- Pick how you know the triangular end: its three sides, or its base and height.
- Enter those values and the prism length in one unit, then select the unit.
- Read the volume; with three sides you also get the lateral and total surface area.
How to read the answer
A prism's volume is the area of one end times the length between the ends. The lateral area is the three rectangular faces, each side-of-triangle × length, so it equals the triangle's perimeter times the length. Total surface area adds the two triangular ends.
Common mistakes and edge cases
- Using a side of the triangle as its height. The height must be perpendicular to the base.
- Three sides that fail the triangle inequality (like 1, 2, 3) cannot form an end and are rejected.
- Forgetting to double the triangle area when adding the two ends to the surface area.
- Mixing up the prism length with the triangle's height — the length runs between the two triangular faces.
Worked examples
3-4-5 triangle, length 10
Volume
60
Equilateral 5-5-5, length 12
Volume
129.9038
Base 6, height 4, length 10
Volume
120
Decimal sides 2.5, 3.5, 4 with length 8
Volume
34.641
Sides 7, 8, 9, short length 2
Volume
53.6656
Impossible triangle 1, 2, 3
Volume
Error
Zero length
Volume
Error
Frequently asked questions
What is the volume of a triangular prism?+
The area of the triangular end times the prism length: V = (½·b·h)·L. A 3-4-5 right-triangle end (area 6) with length 10 gives 60.
What is the surface area of a triangular prism?+
Two triangles plus three rectangles: SA = 2·(triangle area) + (a + b + c)·L. For the 3-4-5 prism of length 10 that is 12 + 120 = 132.
How do I find the area of the triangle if I only know its sides?+
Use Heron's formula: s = (a + b + c)/2 and area = sqrt(s(s−a)(s−b)(s−c)). The calculator does this in the three-sides mode.
Which measurement is the length of the prism?+
The distance between the two triangular ends — how far the triangle is 'stretched'. It is sometimes called the height of the prism, which is why this page calls it length to avoid confusion with the triangle's height.
Can I get the surface area from base and height alone?+
No. The three rectangular faces depend on all three side lengths of the triangle, so switch to the three-sides mode.
Is a triangular prism the same as a pyramid?+
No. A prism has two identical triangular ends joined by rectangles; a pyramid has one base and comes to a point, with one third the volume of the prism with the same base and height.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- September 4, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
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Last updated: September 4, 2026